高精度低时延CORDIC算法  

CORDIC algorithm with high accuracy and low delay

作　　者：揭灿 朱晓宇[1] 赵霁 JIE Can;ZHU Xiaoyu;ZHAO Ji(The 58th Research Institute of China Electronics Technology Group Corporation,Wuxi 214000,China)

机构地区：[1]中国电子科技集团第五十八研究所,江苏无锡214000

出　　处：《现代电子技术》2023年第7期171-175,共5页Modern Electronics Technique

摘　　要：针对目前流水线型坐标旋转数字计算机(CORDIC)算法存在输出精度较低、输出时延较长的问题,提出一种基于移位相加结构的CORDIC算法。此算法首先对[0,π4)内的输入角度采用角度二极化重编码技术,将角度二进制编码转化为1和-1编码,然后使用移位相加结构替代查找表,同时通过合并迭代结构合并旋转迭代,减少迭代单元级数和迭代次数,降低硬件资源的消耗,建立小容量正余弦值ROM表,降低接近于π2时部分输入角度的运算误差,最后结合角度区间映射手段保证算法运算范围覆盖整个圆周[0,2π)。在Xilinx公司KC705评估套件上进行算法验证与仿真,结果表明:在输出位宽都设定为16位的条件下,运算结果的绝对误差和相对误差相比流水线型CORDIC算法分别降低了46.7%,83.5%,该算法只需6个时钟周期即可输出计算结果,输出时延减少了60.0%。设计的CORDIC算法具有输出精度高、输出时延短的优势,适用于实时、高精度的现代通信系统。A coordinate rotation digital computer(CORDIC)algorithm based on shift addition structure is proposed in this paper because the problems that the current pipelined CORDIC algorithm suffers low output accuracy and long output delay.The angle dipolarization recoding technology is used first in the new algorithm for the input angle in[0,π4)to convert the angle binary encoding into 1 and-1 encoding,and then a shift⁃add structure is used instead of a lookup table,while merging rotation iterations by merging iterative structures to reduce the number of iteration unit levels,iterations and the consumption of hardware resources.Moreover,a small⁃capacity sine and cosine value ROM table is established in the proposed algorithm to reduce the calculation error of some input angles while it is close toπ2.The angular interval mapping method is combined to ensure that the calculation range of the algorithm covers the entire circumference[0,2π).Verification and simulation of the algorithm were performed on the Xilinx KC705 evaluation kit.The results show that when the output bit width is set to 16 bits,the absolute and relative errors of the operation results are reduced respectively by 46.7%and 83.5%compared with the pipelined CORDIC algorithm.The algorithm can output the calculation resultin only 6 clock cycles,and the output delay is reduced by 60.0%.The proposed CORDIC algorithm has the advantages of high output accuracy and short output delay.It is suitable for modernreal⁃time communication systems with high precision.

关 键 词：坐标旋转数字计算机 角度二极化重编码 移位相加 合并迭代 角度区间映射 数字信号处理 

分 类 号：TN492-34[电子电信—微电子学与固体电子学] TN914.3